Andrew Flatt, who oversees marketing for Disney’s live entertainment, explains how video and social media have become more vital ways to fill theater seats.

Twenty-five years ago this year, Disney Theatrical Productions launched in advance of its first project, Beauty & the Beast, which debuted on Broadway in 1994. The stage show breathed new life into the Walt Disney Company’s live-entertainment efforts, kicking off a decades-long string of popular musicals from The Lion King and...